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The traceless Ricci tensor $C_{ab}$ in 4-dimensional pseudo-Riemannian spacesequipped with the metric of the neutral signature is analyzed. Its algebraicclassification is given. This classification uses the properties of $C_{ab}$treated as a matrix. The Petrov-Penrose types of Pleba\'nski spinors associatedwith the traceless Ricci tensor are given. Finally, the classification iscompared with a similar classification in the complex case.

Classification of the traceless Ricci tensor in 4-dimensional pseudo-Riemannian spaces of neutral signature